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\(S=\frac{1}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{99.101}\right)\)
\(=\frac{1}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{101}\right)\)
\(=\frac{1}{2}.\left(1-\frac{1}{101}\right)\)
\(=\frac{1}{2}.\frac{100}{101}=\frac{50}{101}\)
=> 2S + 1/101 = \(2.\frac{50}{101}+\frac{1}{101}=\frac{100}{101}+\frac{1}{101}=\frac{101}{101}=1\)
a/ \(-\frac{81}{504}=-\frac{9}{56};-\frac{10101}{101010}=\frac{-1}{10}\)
b/ \(\frac{72\cdot5+72\cdot3}{144\cdot2+144\cdot6}=\frac{72\left(5+3\right)}{144\left(2+6\right)}=\frac{8}{2\cdot8}=\frac{1}{2}\)
\(\frac{-81}{504}=-\frac{81:9}{504:9}=-\frac{9}{56}\)
\(\frac{-10101}{101010}=\frac{-10101:10101}{101010:10101}=\frac{-1}{10}\)
\(\frac{72.5+72.3}{144.2+144.6}=\frac{72.\left(5+3\right)}{144\left(2+6\right)}=\frac{72.8}{144.8}=\frac{72.8}{72.2.8}=\frac{1}{2}\)
( X - 1/2 ) . 5/2 + 1/2 = 7/4
( X - 1/2 ) . 5/2 = 7/4 - 1/2
( X - 1/2 ) . 5/2 = 5/4
X - 1/2 = 5/4 : 5/2
X - 1/2 = 1/2
X = 1/2 + 1/2
X = 1/4
\(\left(x-\frac{1}{2}\right).\frac{5}{2}+\frac{1}{2}=\frac{7}{4}\)
<=>\(\left(x-\frac{1}{2}\right).\frac{5}{2}=\frac{5}{4}\)
<=>\(x-\frac{1}{2}=\frac{5}{4}:\frac{5}{2}\)
<=>\(x-\frac{1}{2}=\frac{1}{2}\)
<=>x=1
a) 7/2.x - (7.(18+45+47))=3
7/2.x - 7.110 = 3
7/2.x - 770 =3 => 7/2.x = 3+770=773
=> x = 773 : 7/2 = 1546/7
b) 19/3 - ( 4x+6x+x)= 4/7 : 2/5
19/3 - 11x = 10/7
11x = 19/3 - 10/7 = 103/21
x = 103/21 : 11 = 103/231
\(\frac{7256.4375-725}{3650+4375.7255}\)
\(=\frac{\left(7255+1\right).4375-725}{3650+4375.7255}\)
\(=\frac{7255.4375+4375-725}{3650+4375.7255}\)
\(=\frac{7255.4375+3650}{3650+4375.7255}\)
\(=1\)
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